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Radiat Res. 2017 Jan;187(1):7-19. doi: 10.1667/RR14520.1. Epub 2017 Jan 13.

Seeking Beta: Experimental Considerations and Theoretical Implications Regarding the Detection of Curvature in Dose-Response Relationships for Chromosome Aberrations.

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a   Center for Radiological Research, Columbia University, New York, New York.
b   Department of Radiation Oncology, University of Texas Medical Branch, Galveston, Texas.


The concept of curvature in dose-response relationships figures prominently in radiation biology, encompassing a wide range of interests including radiation protection, radiotherapy and fundamental models of radiation action. In this context, the ability to detect even small amounts of curvature becomes important. Standard (ST) statistical approaches used for this purpose typically involve least-squares regression, followed by a test on sums of squares. Because we have found that these methods are not particularly robust, we investigated an alternative information theoretic (IT) approach, which involves Poisson regression followed by information-theoretic model selection. Our first objective was to compare the performances of the ST and IT methods by using them to analyze mFISH data on gamma-ray-induced simple interchanges in human lymphocytes, and on Monte Carlo simulated data. Real and simulated data sets that contained small-to-moderate curvature were deliberately selected for this exercise. The IT method tended to detect curvature with higher confidence than the ST method. The finding of curvature in the dose response for true simple interchanges is discussed in the context of fundamental models of radiation action. Our second objective was to optimize the design of experiments aimed specifically at detecting curvature. We used Monte Carlo simulation to investigate the following parameters. Constrained by available resources (i.e., the total number of cells to be scored) these include: the optimal number of dose points to use; the best way to apportion the total number of cells among these dose points; and the spacing of dose intervals. Counterintuitively, our simulation results suggest that 4-5 radiation doses were typically optimal, whereas adding more dose points may actually prove detrimental. Superior results were also obtained by implementing unequal dose spacing and unequal distributions in the number of cells scored at each dose.

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